How did they create their brackets? Two Davidson students explain.

Maddie Parrish is senior Economics major with a Communications Studies concentration at Davidson College. She plays Division I field hockey.

March Madness. 65 elite NCAA Division I Basketball teams competing to win it all, the NCAA Tournament Championship. Every year fans from across the nation create brackets to predict who will ultimately be #1. I am one of those fans, and I’m excited to share my story. My name is Maddie Parrish and I am a senior Economics major with a Communication Studies concentration at Davidson College, a small, highly selective liberal arts school twenty minutes north of Charlotte, NC. We are also the alma mater to such basketball phenoms as John Belk ’43, Terrence Holland ’65, Kenneth Wilson ’84, Mike Maloy, and Stephen Curry. My hometown is Chester, VA, a suburb of Richmond and I have interests in economics, communications, sports, and many other topics. In the fall of 2012, I wrapped up my fourth and final season as a member of the Davidson Wildcats NCAA Division I Field Hockey Team. Being a student-athlete at Davidson has clearly shaped my college experience. It has made me who I am today by teaching me many lessons about dedication, respect, passion, heart, and life in general.

As a student-athlete, the pride I have in my school and its’ athletic teams is enormous. I am a huge fan of college basketball and I am close friends with many of the Davidson Basketball Team members. Our boys just won the 2013 Southern Conference Championship for a second year in a row and the entire school is supporting them in their March Madness journey to the NCAA Championship. My personal connections and interest in Davidson basketball are my main reasons for completing a March Madness bracket this year.

I am an athlete, a sports-lover, and a passionate sports enthusiast. Although a rookie to Bracketology, I know that using mathematic strategies is the best way to create a successful bracket. Being an Economics major, math comes easily to me and I find it very enjoyable. This Spring I am taking Dr. Tim Chartier’s MAT 110 – Finite Math course here at Davidson in which we spend a good chunk of class time learning about linear systems and how to solve them. The concepts of linear systems are the key behind ranking the right teams in our bracket by using matrices and weighted values. In class, we learned about the Colley Method for sports ranking, which utilizes winning percentage to determine each team’s ranking. Another method of sports ranking is the Massey Method, which utilizes actual game scores in the regular season to determine each team’s ranking. With both methods, there is an opportunity to choose your own weighted values for specific times during the season. For example, it is possible to weight games that occurred in the beginning of the season less than games mid-way through the season and at the end of the season. If games at the end of the season are weighted more than 1 game, say each game counts as 2 games; the weight is capturing a team’s final push or momentum. A team’s momentum is explained by their ability to win games at the end of the season, which is admirable because the season is so long and competition may be very tough.

For my March Madness bracket this year, I am choosing to use the Colley Method because I am curious to use my newly learned knowledge from class in a life application and see how well it really works. I split the season into four even intervals, one for games at the beginning of the

season, one for games leading up to mid-way through the season, one for games in the second half of the season, and one for games at the very end of the season. I am creating my weights for each season interval based on the hypothesis that as a basketball team plays more games, it gains momentum and wins more frequently. I also am using the Davidson Men’s Basketball schedule results from this year to create my weights. In the first two intervals of the season, the team lost a good number of games. However, they have not yet lost a game in the third and fourth intervals of this year’s season. Using this intuition, I am weighting the first interval at 0.5/1 game, the second interval at 0.75/1 game, the third interval at 1.25/1 game, and the fourth interval at 2/1 games. This means that games played in the beginning of the season are only worth half of a game and games at the end of the season are worth two games. Therefore, if a team is winning more at the end of the season due to momentum then those wins will be worth more in my ranking method.

I understand that using the Colley Method may not factor in specific scores of games and because of this will not capture strength of opponents throughout the season. Yet, I am confident that using the Colley Method and the particular weights I have chosen will produce solid results. After the 65 teams (1 play-in) were announced on Selection Sunday, I filled in my bracket according my method rankings. Of course, I ranked Davidson higher due to the success of their season thus far and due to my personal bias.

As a student-athlete, I have always been interested in how we can harness the talents of individual teams throughout the nation and celebrate sports through common mediums such as love for the game, competition, and passion for your school. The NCAA Division I Men’s Basketball Tournament provides a venue for all of these values. It also allows for fans to express their passion for the game, pride for their school, and their intuitive math sense in a fun way. Using my intuition as an athlete and my knowledge of math, I have created a bracket that I hope will perform well during the March Madness basketball tournament. I am curious to see how it turns out and wish the best of luck to all of the teams who have the honor and privilege of participating in the tournament! Here at Davidson, we have a saying that runs throughout campus each day that follows “It’s a Great Day to be a Wildcat!” Hopefully, my bracket will sing this tune throughout the tournament! Go ‘Cats!

Kyle Snipes is a senior Math major at Davidson College. He is from Indian Trail, NC. He is a volunteer Younglife leader and a lifelong basketball fan. He will be spending this March Madness season cheering on the Davidson Wildcats!

I have competed in bracket pools for a long as I can remember. In the past I have picked games based on what I know about basketball with a fairly high success rate. Since my senior year of high school, I have won at least one of the couple of pools that I have competed in. This will be my first year applying mathematics to my March Madness selections.

I will use ranking methods adapted from the Colley and Massey ranking methods. Since all NCAA tournament games are played at neutral sites, I will count road and neutral site games as a full game, while weighting home games as partial games to account for any homecourt advantage a team might have during the regular season.

I will weigh different portions of the season differently. Generally teams will play the toughest part of their nonconference schedule in preseason tournaments and standalone nonconference games early in the season. On the other hand, a team’s performance early of the season is less likely to be representative of their performance at the end of the season. Therefore, I will give games during the first quarter of the season a weight of 0.7. The second quarter of the season is still a bit early to be representative of a team’s performance come tournament time. Since there are generally fewer nonconference games during this part of the season, I will give these games a weight of 0.6. Teams begin playing the important part of their nonconference during the third quarter of the season. It is also the point in the season where teams poised to make a deep run in the tournament will begin hitting their stride. I will give the games during this quarter of the season a weight of 0.85. Teams that succeed during the last quarter of the regular season are the teams that will be hot coming into the tournament. I will give these games a weight of 1. I have noticed that teams that rely solely on winning their conference tournaments to get to the Big Dance will be burnt out by the time they play the next weekend. Furthermore, teams that have already secured a spot in the Big Dance may have more of an incentive to rest players and avoid injury than to perform to the best of their potential during their conference tournament, making these games even more illegitimate. Therefore, I will only use data from regular season games in my rankings.

One last idea I would like to implement into my ranking is to reward teams who go on long winning streaks as well as teams who are able to beat teams on long winning streaks. I imagine that this will help pick out teams who are able to win successive games, as they must do in the tournament, as well as the giant killers who are able to beat teams that are in the middle of a strong run. If I have the time, I will do this by incrementing a game’s weight by 0.05 for each game in the winning streak for whichever team comes into the game with a longer winning streak. I will cap this at a weight of 1.5 games to avoid over-rewarding strong teams playing in weak conferences in which long winning streaks are common. I plan on submitting three bracket– two using different ranking methods and one where I will synthesize the math with my intuition. I’m excited to see how my picks stand up against the rest of the country!